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Last year Manfred received 26 paychecks. Each of his first 6

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Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post Updated on: 02 Oct 2016, 21:02
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A
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Question Stats:

76% (01:29) correct 24% (01:35) wrong based on 215 sessions

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Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?

(A) $752
(B) $755
(C) $765
(D) $773
(E) $775

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-manfred-received-26-paychecks-each-of-his-first-168484.html

Originally posted by Madelaine88 on 03 Mar 2011, 06:16.
Last edited by Bunuel on 02 Oct 2016, 21:02, edited 4 times in total.
Renamed the topic and edited the question.
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 03 Mar 2011, 07:38
Madelaine88 wrote:
Last year Manfred received 26 peychecks. Each of his first paychecks was $750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A/ 752
B/ 755
C/ 765
D/ 773
E/ 775


Are you sure about the numbers in the question? It doesn't seem right to me.

Anyway, the approach would be as follows:

One paycheck is 750 and remaining are 30 more, so 780 each.

Hence, average should be (750 + 25*(750+30))/26 = 26*750/26 + 25*30/26 = 750 + ~29 = ~779.
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 03 Mar 2011, 10:31
Last year Manfred received 26 peychecks. Each of his first six paychecks was $750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?


first 6 paychecks was 750 = 6(750) = 4500
remaining paychecks (26-6 = 20) was 30 more = 20(750+30) = 15600
so 4500+15600/26 = 773
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 25 Apr 2011, 03:42
Can the balancing method be used here? I am sure it can but not sure how....Can anyone help?

thanks
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 25 Apr 2011, 04:11
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1
Madelaine88 wrote:
Last year Manfred received 26 peychecks. Each of his first six paychecks was $750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A/ 752
B/ 755
C/ 765
D/ 773
E/ 775


R1: 750/check
W1: 6

R2: 780/check
W2: 20

R1-----W2----Avg------W1-----R2
750-----20----Avg------6-----780

20/6 = 10/3

750-----10----Avg------3-----780

780-750=30.

(10/13)*30=300/13=23 Approx
750+23=773= Avg

OR

(3/13)*30=90/13=7
780-7=773=Avg

Ans: "D"
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 25 Apr 2011, 06:00
= (750*6+ 780 *20)/26
= 773

Answer is D.

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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 26 Apr 2011, 07:14
2
Madelaine88 wrote:
Last year Manfred received 26 peychecks. Each of his first six paychecks was $750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A/ 752
B/ 755
C/ 765
D/ 773
E/ 775


If M had received $750 for rest of the 20months as well, avg would have been $750. Since he received $30 more each month for 20months, total "extra" amount is $600.

$600 averaged over 26 paycheck = 600/26 ~ 23.
Hence total avg: 750+23 = 773

OA. D
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 26 Apr 2011, 07:26
First 6 paychecks = $750, hence total is 750*6 = $4500
Next 20 paychecks = $780, hence total is 780*20 = $15600
Total = $20100. Hence monthly average = 20100/26 = 773
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 26 Apr 2011, 20:00
Madelaine88 wrote:
Last year Manfred received 26 peychecks. Each of his first six paychecks was $750; each of his remaining paychecks was $30 more than each of his first paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

A/ 752
B/ 755
C/ 765
D/ 773
E/ 775


Total paychecks: p = 26
6 has $750 each: 6 x 750 = 4500
20 has $750 + $30: 20 x 780 = 15,600

(4500 + 15,600)/26 = 773
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 26 Apr 2011, 20:09
After solving and reading all your solutions, I think your solution is faster. I take 30 x20 = 600 and spread it to all the 26 750s.

600/26 (approx) ~ 23
So Average is 750 +23 = 773
Answer is sitll the same D... better solution..(y)
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 27 Apr 2011, 21:47
8
1
Using Weighted Average,

[ (0) * (6) + (30) * (20)] / 26 = 23.07

hence, average = 750 + 23.07 = 773 approx.
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 18 Oct 2013, 08:16
For simplicity I took out 0's from 750 and 780.

75 -------------------------------------- 78
(6- make these 5) ------------------- (20)
5:20 = 1:4

average will be 1/5 th unit below 78 . i.e (1/5)*3 = 0.6 . Hence 77.4 .Will be slightly less since we took 5 instead of 6 for 75.
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 22 Feb 2014, 19:44
I chugged through this slow, upon review, would have been quicker to recognise, in the same way as above;

$30*20/26

Round to 4/5 of 30 = $24. $750+$24 = $774. 20/26 slightly smaller than 4/5, so go with $773.
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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New post 02 Oct 2016, 21:03
Madelaine88 wrote:
Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?

(A) $752
(B) $755
(C) $765
(D) $773
(E) $775


Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

(A) $752
(B) $755
(C) $765
(D) $773
(E) $775

The average amount of the paychecks =

\(\frac{750*6+ (750 +30)*20}{26}=\frac{750*26+ 30*20}{26}=750+\frac{30*20}{26}=750+\frac{30*10}{13}\approx{750+23}=773\).

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-year-manfred-received-26-paychecks-each-of-his-first-168484.html
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Re: Last year Manfred received 26 paychecks. Each of his first 6  [#permalink]

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